# Enumerating meandric systems with large number of loops

@inproceedings{Fukuda2016EnumeratingMS, title={Enumerating meandric systems with large number of loops}, author={Motohisa Fukuda and Ion Nechita}, year={2016} }

We investigate meandric systems with a large number of loops using tools inspired by free probability. For any fixed integer $r$, we express the generating function of meandric systems on $2n$ points with $n-r$ loops in terms of a finite (the size depends on $r$) subclass of irreducible meandric systems, via the moment-cumulant formula from free probability theory. We show that the generating function, after an appropriate change of variable, is a rational function, and we bound its degree… CONTINUE READING

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